Due to the movement of the camera relative to the scene, the images taken often suffer motion blur to some extent. The image degradation model can be expressed as a convolution process as follows:I=L⊗k+N, wherein I represents the acquired blurred image, L represents a clear image, k is a blur kernel (i.e. Point Spread Function (PSF)), and N represents the noise generated by the image acquisition device. Since only the blurred image I is known, the process to restore a clear image L from a blurred image is a large-scale ill-posed inverse problem.
As motion de-blurring of a single image is valuable to many applications, it has attracted much attention. There have been various motion de-blurring algorithms to solve the ill-posed problem of obtaining a clear image L. For example, Fergus et al. expressed the long-tailed distribution model of the gradient of natural image as a Gaussian Mixture Model (GMM), which was used for constraining the clear image L. The clear image L was obtained by using the ensemble learning method. Shan et al. expressed the long-tailed distribution as a piecewise function to constrain the gradient of the clear image L. Krishnan et al. assumed that the gradient of the clear image L followed the hyper-Laplacian distribution, and obtained a high-quality reconstructed image. The hyper-Laplacian constraint is widely used as a valid constraint in later de-blurring works. Pan et al. constrained the clear image L and the blur kernel k by using a low-rank constraint term and the Gaussian regularization term respectively. Although the continuity of the blur kernel k is guaranteed to some extent, the use of a threshold parameter to remove noise in blur kernel k also affects its continuity.
Moreover, the selection of the salient edge of image largely affects the accuracy of blur kernel k estimation. Research has found that accurate blur kernel estimation can be obtained only in images in which the edge sizes are larger than the scale of the blur kernel k; otherwise, blur kernel estimation becomes inaccurate. Hence, the selection of proper edge information is critical to blur kernel estimation. Cho and Lee extracted sharp edges with bilateral filters and shock filters, but it was difficult to control the scale of the edges, thus was detrimental to the estimation of blur kernel k. Xu and Jia proposed a method for measuring the scale of the edge, which could effectively extract useful salient edges. Pan et al. made an improvement based on the salient edge selection method, which made selected edges more effective. Unlike the dedicated salient edge extraction method, Xu and Pan et al. used l0 constraint to maintain the main structure in the restored intermediate image L for blur kernel k estimation and achieved good results.
However, many problems remain in both blur kernel estimation and non-blind deconvolution in the final image, and it is necessary to further improve the effect of image de-blurring.